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Results tagged with set-theory
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user 90758
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
2
votes
1
answer
311
views
Does every elementary embedding $j:V \to V$ in ZFA arise from a self-injection on the class ...
When atomhood is definable, the answer is clearly yes, so essentially the question is interesting primarily when we are working in ZF with extensionality weakened to apply only to inhabited sets. In t …
- 218
8
votes
Accepted
How much Replacement does this axiom provide?
Asaf points out that Axiom A is true in $V_{\delta}$ if $\delta$ is a $\beth$ fixed point. Full replacement only holds if $\delta$ is worldly. So, in $V_{\delta}$ models of these, replacement implies …
- 218